The height in an isosceles trapezoid

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Question from Riham:

Hi
How can I find the height in an isosceles trapezoid if I have the measurements of all of its sides ?
Thank u in advance.

Hi,

Suppose the length of the longer of the parallel sides is $L$ units, the length of the shorter of the parallel sides is $S$ units and the lengths of the other two sides is $x$ units as in the diagram below.

trapezoid

The length of the line segment BC is $\large \frac{L-S}{2},$ can you see why? Thus for the right triangle $ABC$ you know the lengths of two of its sides and Pythagoras Theorem will give you $h,$ the length of the third side.

Penny

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